1. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
SOLUTION
7p + 13 = 9p – 5
Write original equation.
13 = 2p – 5
Subtract 7p from each side.
18 = 2p
Add 5 to each side.
9 = p
Divide each side by 2.
ANSWER
The correct answer is D

2. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
CHECK
7p + 13 = 9p – 5
Write original equation.
7(9) (9) – 5 = ?
Substitute 9 for p.
– 5 = ?
Multiply.
76 = 76
Solution checks.

3. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
Solve 3(5x – 8) = – 2(– x + 7) – 12x.
3(5x – 8) = – 2(– x + 7) – 12x
Write original equation.
15x – 24 = 2x – 14 – 12x
Distributive property
15x – 24 = – 10x – 14
Combine like terms.
25x – 24 = –14
Add 10x to each side.
25x = 10
Add 24 to each side.
x = 2 5
Divide each side by 25 and simplify.
ANSWER
The solution 2 5

4. Solve an equation using the distributive property
EXAMPLE 4
Solve an equation using the distributive property
CHECK
3 ( – 8) – 2(– ) – 12 2 5 = ? 2 5
Substitute for x.
3( – 6) –14 – 4 5 = ? 24
Simplify.
– 18 = – 18
Solution checks.

5. EXAMPLE 5
Solve a work problem
Car Wash
It takes you 8 minutes to wash a car and it takes a friend 6 minutes to wash a car. How long does it take the two of you to wash 7 cars if you work together?
SOLUTION
STEP 1
Write a verbal model. Then write an equation.

6. Solve the equation for t. STEP 2 1 8 t + t = 7 6 24( t + t) = 24 (7) 1
EXAMPLE 5
Solve a work problem
Solve the equation for t.
STEP 2 1 8
t t = 7 6
Write equation.
24( t + t) = 24 (7) 1 8 6
Multiply each side by the LCD, 24.
3t + 4t = 168
Distributive property
7t = 168
Combine like terms.
t = 24
Divide each side by 7.
ANSWER
It will take 24 minutes to wash 7 cars if you work together.

7. EXAMPLE 5
Solve a work problem
CHECK
You wash = 3 cars and your friend washes = 4 cars in 24 minutes. Together, you wash 7 cars. 1 6 8

8. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
5. –2x + 9 = 2x – 7
SOLUTION
–2x + 9 = 2x – 7
Write original equation.
–4x + 9 = – 7
Subtract 2x from each side.
–4x = –16
subtract 9 from each side.
x = 4
Divide each side by –4.
ANSWER
The correct answer is 4.

9. GUIDED PRACTICE for Examples 3, 4, and 5 CHECK –2(4) + 9 2(4) – 7 =
–2(4) (4) – 7 ? =
Substitute 4 for x.
–8 + 9 = 8 – 7
Simplify
1 = 1
Solution check

10. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
– x = – 6x + 15
SOLUTION
10 – x = – 6x + 15
Write original equation.
10 + 5x = 15
Add 6x to each side.
5x = 5
subtract 10 from each side.
x = 1
Divide each side by –5.
ANSWER
The correct answer is 1.

11. GUIDED PRACTICE for Examples 3, 4, and 5 CHECK 10 –1 – 6(1) + 15 =
10 –1 – 6(1) + 15 ? =
Substitute 1 for x.
9 = 9
Solution check.

12. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
(x + 2) = 5(x + 4)
SOLUTION
3(x + 2) = 5(x + 4)
Write original equation.
3x + 6 = 5x + 20
Distributive property.
6 = 2x + 20
Subtract 3x from each side.
– 14 = 2x
Subtract 20 from each side.
x = –7
Solve for x
ANSWER
The solution is –7.

13. GUIDED PRACTICE for Examples 3, 4, and 5 CHECK 3((–7) + 2) 5 (–7 + 4)
3((–7) + 2) (–7 + 4) ? =
Substitute – 7 for x.
3(–5) (–3) ? =
Simplify
– 15 = –15
Solution check.

14. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
8. – 4(2x + 5) = 2(– x – 9) – 4x
SOLUTION
– 4(2x + 5) = 2(–x – 9) – 4x
Write original equation.
–8x – 20 = –2x – 18 – 4x
Distributive property.
–8x – 20 = –6x – 18
Combine like term.
–20 = 2x – 18
Add 8x to each side.
–2 = 2x
Add 18 to each side.
x = –1
Divide each side by 2.

15. GUIDED PRACTICE for Examples 3, 4, and 5 ANSWER The solution x = – 1
CHECK
–4 (2(–1) + 5 ) 2(–(–1) – 9) – 4(–1) = ?
Substitute –1 for x.
– 4( – 2 + 5) (– 8) + 4 = ?
Simplify.
– 4( 3) (–16) + 4 = ?
– = –12
Solution checks.

16. Solve the equation. Check your solution.
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
x x = 39 1 4 2 5 9.
SOLUTION
x x = 39 1 4 2 5
Write original equation.
13x 20
= 39
Combine like term.
13x =
Multiply each side by 20.
x = 60
Divide each side to 13.
ANSWER
The correct answer is 60

17. GUIDED PRACTICE for Examples 3, 4, and 5 CHECK x + x = 39 1 4 2 5 1 4
Write original equation. 1 4
(60) (60) 2 5 ? =
Substitute 60 for x. ? =
120 5 + 60 4 39
Simplify
39 = 39
Solution checks. 

18. GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation. Check your solution.
x = x – 1 2 3 5 6
ANSWER
The correct answer is 4

19. GUIDED PRACTICE
for Examples 3, 4, and 5
What If? In Example 5, suppose it takes you 9 minutes to wash a car and it takes your friend 12 minutes to wash a car. How long does it take the two of you to wash 7 cars if you work together?
11.
SOLUTION
STEP 1
Write a verbal model. Then write an equation.
t min
1 car
9 min
12 min
t min = 7 +

20. Solve the equation for t. STEP 2 1 9 t + t = 7 12 36( t + t) = 36 (7)
GUIDED PRACTICE
for Examples 3, 4, and 5
Solve the equation for t.
STEP 2 1 9
t t = 7 12
Write equation.
36( t + t) = 36 (7) 1 9 12
Multiply each side by the LCD, 24.
4t + 3t = 252
Distributive property
7t = 252
Combine like terms.
t = 36
Divide each side by 7.
ANSWER
It will take 36 minutes to wash 7 cars if you work together.

21. EXAMPLE 5
GUIDED PRACTICE
for Examples 3, 4, and 5
CHECK
You wash = 4 cars and your friend washes = 3 cars in 36 minutes. Together, you wash 7 cars. 1 12 9